$($A$)$ A $12-$station automated production line has an ideal cycle time of $30$ sec$.$ Line stops occur on average once every $20$ cycles. When a line stop occurs, average downtime is $4\mathrm{.}0$ min. Cost of each starting work part is $$1\mathrm{.}55,$ and the cost to operate the line is $$66/$hr$.$ Tooling cost is $$0\mathrm{.}27$ per work part. Determine $($a$)$ average hourly production rate, $($b$)$ line efficiency, and $($c$)$ cost of a workpiece produced.